Notation conventions

Physics uses precise mathematical symbols: distinguishing a scalar from a vector is not a detail, it is part of the meaning. The book adopts the following conventions, kept consistent from the first to the last chapter, so that a symbol always has the same meaning wherever it appears.

• Scalars: italic letters, $v$, $E$, $T$. They denote quantities that have only magnitude, i.e. a number with a unit of measurement.
• Vectors: upright bold letters, $\pq{F}$, $\pq{v}$, $\pq{B}$. The symbol $\pq{F}$ represents force as a vector (magnitude + direction + sense). When only the magnitude matters, it is written $\abs{\pq{F}}$ or simply $F$.
• Unit vectors: upright hat, $\vers{x}$, $\vers{r}$. They are vectors of unit magnitude that indicate only a direction.
• Matrices and operators: bold capital letters, such as $\pq{R}$ for the rotation matrix (rarely used in this text).
• Number sets: double-struck, $\R$ (reals), $\N$ (naturals), $\Z$ (integers), $\Q$ (rationals).
• Differentials: $\dd t$, $\dd x$ in upright type, to distinguish them from variables.

Numbers and units

For units of measurement the book follows the International System (the siunitx package): the number and the unit are separated by a thin non-breaking space. Examples: $9{,}8\;\mathrm{m/s}^2$, $3{,}0\cdot 10^8\;\mathrm{m/s}$. The decimal comma follows Italian usage; for powers of ten the notation $a\cdot 10^n$ is used.

These choices are not a graphic affectation: the difference between $F$ (a number) and $\pq{F}$ (a vector) can completely change the meaning of an equation, and a forgotten unit is almost always the sign of a reasoning error.

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